A262613 Sum of divisors of n-th generalized pentagonal number.

1, 3, 6, 8, 28, 24, 36, 42, 48, 90, 72, 80, 144, 96, 168, 217, 182, 312, 180, 192, 372, 216, 576, 456, 280, 588, 336, 352, 864, 576, 720, 855, 558, 756, 702, 936, 1120, 600, 1080, 1116, 1024, 2016, 1008, 816, 1296, 1152, 2016, 2072, 1178, 1860, 1344, 1120, 3600

Offset

1,2

Comments

For a remarkable connection between the sum-of-divisors function (A000203) and the generalized pentagonal numbers (A001318) see A238442.

Links

Antti Karttunen, Table of n, a(n) for n = 1..5000

Formula

a(n) = A000203(A001318(n)).

Sum_{k=1..n} a(k) ~ (9/40) * n^3. - Amiram Eldar, Dec 14 2024

Mathematica

DivisorSigma[1, Select[Accumulate[Range[200]]/3, IntegerQ]] (* G. C. Greubel, Jun 06 2017 *)

Prog

(Scheme)
(define (A262613 n) (A000203 (A001318 n))) ;; Scheme-program for A000203 given in that entry.
;; This uses memoization-macro definec:
(definec (A001318 n) (if (zero? n) 0 (+ (if (even? n) (/ n 2) n) (A001318 (- n 1)))))
;; Antti Karttunen, Dec 20 2015
(PARI) a(n) = sigma((3*n^2 + 2*n + (n%2) * (2*n + 1)) / 8); \\ Michel Marcus, Dec 21 2015
(Magma) [DivisorSigma(1, (3*n^2+2*n+(n mod 2)*(2*n+1)) div 8): n in [1..70]]; // Vincenzo Librandi, Dec 21 2015

Crossrefs

Cf. A000203, A001318, A074285, A117948, A196020, A238442.

Sequence in context: A038064 A093899 A306157 * A137129 A098106 A059361

Adjacent sequences: A262610 A262611 A262612 * A262614 A262615 A262616

Keyword

nonn,easy

Author

Omar E. Pol, Nov 24 2015

Status

approved